cours/mesure sigma finie.md
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---
aliases:
- sigma-finie
- σ-finies
---
up:: [[mesure finie]]
#s/maths/intégration
> [!definition] [[mesure sigma finie]]
> Soit $(E, \mathcal{A})$ un [[espace mesurable]]
> Une mesure $\mu$ est dite σ-finie (sigma-finie) si :
> $\boxed{\displaystyle\exists (A_{n}) \in \mathcal{A}^{\mathbb{N}}\text{ croissante}, \quad \mu(A_{n}) < +\infty \quad \wedge \quad \bigcup _{n}A_{n} = E}$
^definition
# Propriétés
# Exemples